"Install to Hard Drive" does nothing when running CentOS LiveCD in VirtualBox

After booting into a new virtual machine in VirtualBox using the CentOS 6.5 live CD for the first time, I tried clicking the "Install to Hard Drive" button. However, the operating system didn't respond.

The issue ended up being that not enough memory was allocated to the virtual machine (it's 512MB by default). Bumping it up to 2048MB solved the issue.